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A preconditioner defined by an algebraic multigrid cycle for a damped Helm-holtz operator is proposed for the Helmholtz equation. This approach is well-suited for acoustic scattering problems in complicated computational domains and with varying material properties. The spectral properties of the precondi-tioned systems and the convergence of the GMRES… (More)

Efficient numerical methods for pricing American options using Heston's stochastic volatility model is proposed. Based on this model the price of a Eu-ropean option can be obtained by solving a two-dimensional parabolic partial differential equation. For an American option the early exercise possibility leads to a lower bound for the price of the option.… (More)

- Raino A E M Akinen, Jari Toivanen, Jacques Periaux, John Wiley
- 1998

A multiobjective multidisciplinary design optimization (MDO) of two-dimensional airfoil is presented. In this paper, an approximation for the Pareto set of optimal solutions is obtained by using a genetic algorithm (GA). The rst objective function is the drag coeecient. As a constraint, it is required that the lift coeecient is above a given value. The CFD… (More)

Stochastic volatility models lead to more realistic option prices than the Black-Scholes model which uses a constant volatility. Based on such models a two-dimensional parabolic partial differential equation can derived for option prices. Due to the early exercise possibility of American option contracts the arising pricing problems are free boundary… (More)

The deterministic numerical valuation of American options under Heston's stochastic volatility model is considered. The prices are given by a linear com-plementarity problem with a two-dimensional parabolic partial differential operator. A new truncation of the domain is described for small asset values while for large asset values and variance a standard… (More)

- S. Ikonen, J. Toivanen
- 2004

Option pricing models with a stochastic volatility are more realistic than the Black-Scholes model which uses a constant volatility. The prices of options based on such models can be obtained by solving a parabolic partial differential equation. Particularly, we consider the model presented by Heston. The variables in these problems are the time, the… (More)